Calculating the Strength of an AES-256 Cipher 

The Advanced Encryption Standard is the de-facto method for securing your data on the internet today. Encryption is a method of "encoding" your data, using a special code called a key, and a complex mathematical operation, to make your data unreadable to anyone without said key. Cracking AES encryption requires you to be able to "guess" the key. Now, guessing a simple key would be easy. A key using a single bit would be a single binary digit. Which is a "1" or a "0". However, the difficulty grows as the length of the key grows. A 5-bit key would have 32 possibilities. This is because for each bit you add, you are doubling the complexity of the key.

The 5-bit key could have the following possible values:

00000    00001    00011    00111    01111    11111

00010    00110    01110    11110    00100    01100

11100    01000    11000    10000    and so on...

So, one can imagine how complex it is to guess a 256-bit key. Well... Not really. It is a number so large that most of us can't even wrap our heads around it.



















     
There are 2^256 or: 

115,792,089,237,316,195,423,570,985,008,687,907,853,269,984,665,640,564,039,457,584,007,913,129,639,936

possible unique keys. That number is read as 115 quattuorvigintillion, 792 trevigintillion, 89 duovigintillion, 237 unvigintillion, 316 vigintillion, 195 novemdecillion, 423 octodecillion, 570 septendecillion, 985 sexdecillion, 8 quindecillion, 687 quattuordecillion, 907 tredecillion, 853 duodecillion, 269 undecillion, 984 decillion, 665 nonillion, 640 octillion, 564 septillion, 39 sextillion, 457 quintillion, 584 quadrillion, 7 trillion, 913 billion, 129 million, 639 thousand and 936.

This number is larger than the number of visible atoms in the known universe. Inconceivably huge.

We recently reported on a man who had leveraged 5 servers and 25 graphics cards, as well as some custom OpenCL code with the help of mathemeticians and researchers, to build a monster hasher that could chew through 348 billion hashes (key guesses) per second. This monstrous acheivement was enough to make 14+ year old encryption schemes unsafe. However, at that rate, it would take epixoip a little under 766,230,000,000,000,000,000,000,000,000,000,000,000,000,000,000 MULTIPLIED BY THE AGE OF THE UNIVERSE to break AES-256. Once.

Even if we took the Titan Supercomputer, the most powerful Open-CL ready supercomputer in the world, and did an estimate of it's hashing power... 1688 Nvidia Tesla K20X units. At an ideal 6.2 billion hashes per second per unit. We still get a result that is a 46-digit number multiplied by the age of the universe.

It is safe to say that, properly implemented, the entire worlds computing power combined could not solve a single key in a lifetime. Or even the lifetime of the universe...

This is why AES-256 is the world standard for strong encryption.









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